﻿Magnetic Field of an Atom. 47 



Substituting the value of t in terms of a previously 

 obtained, we find that the frequency is given by the approxi- 

 mate formula 



where 



„ SAMEr 2 35 167T ? 'mME^ 2 . 



B = ¥ + "2=~ J?~ =b ' 



We may note that equation (17) is equivalent to 



2ir 2 me 2 W (I 1 ~) „ Q . 



v = -^r- i^-T?j- • • • < 18 > 



The formula proposed by Ritz to represent spectral series 

 may be written 



v=v "ih~i} i • • • • (19) 



where D is of the form in + fj, + /3jm 2 or m + f* + /3/(m + fi)' 2 , 

 and z^ is the frequency corresponding to Rydberg's constant. 

 When E = e, that is when the core carries a charge 

 equivalent to the loss of one electron, the factor outside the 

 bracket in equation (17) reduces to 27r 2 me 4: /h 3 , which Bohr 

 identifies with v . The bracket becomes identical in form 

 with that in the formula of Ritz if we take a-=m+fi and 



*=#: .... 



This implies that <r, instead of being an exact integer (in), 

 as in Bohr's theory, is equal to an integer plus a certain 

 fractional quantity /jl, which depends on the element and on 

 the particular series considered. The presence of this 

 fractional part must be assumed ; it is not explained by the 

 action of magnetic forces. 



We conclude that, on the assumptions stated, we can 

 account for the existence of four sequences in spectral series, 

 the denominator of each sequence being of the form proposed 

 by Ritz, and we can determine the lines in a spectral series 

 by the difference between two sequences. 



When, however, we examine the numerical value of the 

 constant /3 as given by Ritz, we find that the values obtained 

 for the magnetic moment M by identifying Ritz's contra nt 

 with the 8 of our analysis are many times too large to be 

 possible. Thus taking for illustration the case of lithium, 

 Ritz gives for {3 in the principal series the value 0*0257, 

 which would correspond with M = 4'5 x 10~ 1S E.M.U. The 

 magnetic moment of the maimeton is l'$~,± x 10~ 31 E.M.U. 



